Russia and China disagree with you. The French and American troubles with building new nuclear plants is more linked to the demise of the state-driven industry in those countries than to some inherent difficulties with nuclear itself.
Plenty of opportunity for cost cutting.
This is incorrect.
The serious design flaw was that the 'stop the reactor reacting' button rapidly accelerated the reaction briefly, but long enough to cause a massive spike.
There were also human errors on the operations side.
Anatoli Diatlov gave INSANE orders that led to the catastrophe. With such a culture were an all powerful chief can send his technicians to gulag if they dare disobeying an accident like this could have happened even with the safest PWR.